The reasonable domain for the function representing the amount of money raised based on the number of tickets sold would be option (1) {0, 1, 2, 3, ...}, consisting of non-negative integers.
Reasonable domain for the scenario
The function m=3n represents the amount of money raised (m) based on the number of tickets sold (n). In this case, the number of tickets sold (n) cannot be negative or fractional, as you can't sell a negative number of tickets or a fraction of a ticket.
So, the domain should be a set of non-negative integers, representing the possible whole number values for the number of tickets sold.
Among the options provided:
(1) {0, 1, 2, 3, ...}: This set represents non-negative integers and is a reasonable domain for the function.
(2) {0, 3, 6, 9, ...}: This set contains multiples of 3, which corresponds to the possible number of tickets sold. It's reasonable as it only includes non-negative integers, multiples of 3 in this case.
(3) (1.5, 3, 4.5, 6, 7.5, ...): This set includes fractional values, which is not suitable as the number of tickets sold should be a whole number.
(4) {... -2, -1, 0, 1, 2, ...}: This set includes negative integers, which is not appropriate since the number of tickets sold cannot be negative.
So, the reasonable domain for the function representing the amount of money raised based on the number of tickets sold would be option (1) {0, 1, 2, 3, ...}, consisting of non-negative integers.